Hi,
I have a direct graph of interactions among internet users. I am looking
for a statistic to capture the level of reciprocity/mutuality of each
node.
In other words, in a graph g, the edges connected to a vertex v can be
of three types: mutual, asymmetric x -> v or asymmetric v -> x. I can
thing of two different statistics which could give you an idea of the
"prestige" of the node:
out.reciprocity = sum(is.mutual(g, E(g)[from(V(g)[v]), na.rm = TRUE)
/ degree(g, E(g)[v], mode="out")
and
in.reciprocity = sum(is.mutual(g, E(g)[to(V(g)[v]), na.rm = TRUE) /
degree(g, E(g)[v], mode="in")
Would make sense to combine these two (in.reciprocity/out.reciprocity)
to obtain a measure of node "prestige"?
Is there exist any other function that will do a better job?
Thanks
Francesco
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